From Consensus to Echo Chambers: Opinion Dynamics with Memory (Spring 2027)


The voter model is one of the simplest models of opinion dynamics, that is, of how opinions spread through a network. In discrete time it can be described as follows: every vertex of a graph holds an opinion, say 0 or 1 (variants allow more opinions). At each step a uniformly random vertex is chosen; it picks one of its neighbors at random and copies that neighbor’s opinion [2]. On a finite connected graph the process eventually reaches consensus, and much is known about which opinion wins and how long it takes.


In this project we give the vertices memory: each vertex keeps an affinity score for each of its neighbors, chooses whom to copy with probability proportional to this score, and updates its affinity for the neighbor it consulted according to a pre-specified rule. With fixed scores this is the voter model on a weighted network [1]; here the scores evolve with the dynamics, in the spirit of reinforced random processes such as Polya urns [3]. Over time each vertex comes to rely on a few favorite neighbors, and when affinity grows mainly towards like-minded neighbors, echo chambers may form. We will explore how memory changes the outcome: how long consensus takes, which vertices end up most influential (depending on the geometry of the network), and whether consensus can fail altogether.


We will start with background reading on the voter model. We will then write efficient simulation code (in Python or R) and explore the model on a ladder of graphs (complete graphs, trees, lattices, and random networks), looking for patterns. Finally, we will analyze tractable cases rigorously and aim to derive concrete results.


For more information contact Souvik Ray (souvikr@iastate.edu)

People:

Pre-requisites:

References:

[1] A. Baronchelli, C. Castellano and R. Pastor-Satorras. Voter models on weighted networks. Phys. Rev. E 83 (2011), 066117.

[2] C. Castellano, S. Fortunato and V. Loreto. Statistical physics of social dynamics. Rev. Mod. Phys. 81 (2009), 591–646.

[3] R. Pemantle. A survey of random processes with reinforcement. Probab. Surveys 4 (2007), 1–79.